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The NYPD cop who posted racist rants on Facebook — one calling the mayor’s wife a “former crack addict” — was one of the officers caught on video dancing suggestively with semi-nude women at the West Indian Day Parade, The Post has learned.

Detective Gregory Gordon, 33, was among several officers captured in the video bumping and grinding with buxom, scantily clad dancers marching in the parade on Sept. 5, 2011, on Eastern Parkway in Crown Heights, sources said.

“He’s the same guy that got in trouble for dancing at the West Indian Day Parade,” a source said.

An enthusiastic Gordon could be seen in the video, which went viral at the time, thrusting against women bent over in front of him as he pumped his arms up and down.

Police opened an investigation into the dirty dancing, and ultimately transferred the cop, a Marine who served in Iraq, from his Brooklyn precinct to the Staten Island one closer to his home.

“We get danced on nonstop at that parade, he was having fun and showing that cops can be fun, too,” the source said in his defense.